## A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of the Nature and Use of Logarithms. Being the Second Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges ... |

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**quadrant**, and con- tains 90 degrees . 74. To measure an angle , a circle is so described that its centre shall be the angular point , and its periphery shall cut the two lines which include the angle . The arc between the two lines is ... Page 41

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**quadrant**ACH , ( Fig . 3. ) these lines form three similar triangles , viz . ACD , BCG or LCG , and HCF . For , in each of these , there is one right angle , because the sines and tangents are , by definition , perpendicular to AC ; as ... Page 43

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**quadrant**ACH , ( Fig . 5. ) the arc AH is 90o . The sine of this , according to the definition , ( Art . 82. ) is CH , the radius of the circle . Then the angle ACS , be- 2. Let AS be an arc of 60 ° . ing measured by this arc , will ... Page 45

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**quadrant**, and arranged in tables . These constitute what is called the Trigonometrical Canon . * It is not ...**quadrants**of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And in ... Page 46

... any given angle within the

... any given angle within the

**quadrant**is greater than 45 ° , its * Or the tables may be supposed to be calculated to the radius 10000000000 , whose logarithm is 10 . complement is less ; and , on the other hand 46 THE TRIGONOMETRICAL.### Other editions - View all

### Common terms and phrases

acute angle added angle ACB arithmetical complement arithmetical progression b+sin base calculation centre circle cosecant Cosine Cotangent Tangent decimal degrees and minutes divided division divisor equal to radius equation errour exponents extend find the angles find the logarithm fraction geometrical progression given angle given number given side Given the angle gles greater half the sum hypothenuse JEREMIAH DAY length less line of chords line of numbers lines of sines loga logarithmic sine logarithmic TANGENT metical Mult multiplied natural number natural sines number of degrees opposite angles perpendicular positive proportion quadrant quotient radix right angled triangle rithms root secant similar triangles sine of 30 sines and cosines slider square subtracting tables tabular radius tabular sine tangent of half theorem transverse distance triangle ABC trigonometrical tables Trigonometry versed sine vulgar fraction

### Popular passages

Page 68 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.

Page 105 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.

Page 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.

Page 39 - With these the learner should make himself perfectly familiar. 82. The SINE of an arc is a straight line drawn from one end of the arc, perpendicular to a diameter which passes through the other end. Thus BG (Fig.

Page 116 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 37 - The periphery of every circle, whether great or small, is supposed to be divided into 360 equal parts called degrees, each degree into 60 minutes, each minute into 60 seconds, each second into 60 thirds, &c., marked with the characters °, ', ", '", &c. Thus, 32° 24...

Page 72 - ... angle. The third angle is found by subtracting the sum of the other two from 180° ; and the third side is found as in Case I.